Question

List the first 4 terms of a geometric sequence with the first term of 2 and a common ratio of 5.

Answer 1

2, 10, 50, 250

Explanation:

For geometric sequences, multiply the previous term by the common ratio.

Using the formula for geometric sequences
`a_(n) =ar^(n-1)` , with
`a_(n)` being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.

Our starting term is 2. So that is automatically the first term of the four.

Second term:

`a_(2) =2*5^(2-1)=2*5^1=2*5=10`

Third term:

`a_(3) =2*5^(3-1)=2*5^2=2*25=50`

Fourth term:

`a_(4) =2*5^(4-1)=2*5^3=2*5*5*5=10*25=250`